Abstract
In this paper, we focus on a recently introduced problem in the context of spatial and temporal qualitative reasoning, called the MAX-QCN problem. This problem involves obtaining a spatial or temporal configuration that maximizes the number of satisfied constraints in a qualitative constraint network (QCN). To efficiently solve the MAX-QCN problem, we introduce and study two families of encodings of the partial maximum satisfiability problem (PMAX-SAT). Each of these encodings is based on, what we call, a forbidden covering with regard to the composition table of the considered qualitative calculus. Intuitively, a forbidden covering allows us to express, in a more or less compact manner, the non-feasible configurations for three spatial or temporal entities. The experimentation that we have conducted with qualitative constraint networks from the Interval Algebra shows the interest of our approach.
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